Bundle: Managerial Economics, 4th + Mindtap Economics, 1 Term (6 Months) Access Code
4th Edition
ISBN: 9781305618572
Author: Luke M. Froeb, Brian T. McCann, Michael R. Ward, Mike Shor
Publisher: Cengage Learning
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Chapter 3, Problem 4MC
To determine
The reason for arising
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Problem 3
Stata Output Analysis
Suppose a study investigates the causal effect of education on wages.
Table 1 reports the results of an OLS regression of wages (wage per hour in dollars) on
education (years in education).
Table 1
Source
SS
df
MS
Number of obs
=
3,017
F(1, 3015)
=
298.39
Model
Residual
18904467
191011981
1
18904467
3,015 63353.8909
Prob > F
0.0000
R-squared
0.0901
Adj R-squared
0.0898
Total
209916448
3,016 69600.9444
Root MSE
251.7
wage
Coef. Std. Err.
t
P>|t|
[95% Conf. Interval]
education
cons
29.56644
183.9342
1.711605
23.15976
17.27 0.000
7.94 0.000
26.21041
138.5237
32.92247
229.3447
a. How would you write this relationship using the Core Model? (5 points)
b. What is the value for B₁, the coefficient on Education? (2 points)
C. What is the standard error of ẞ₁? (2 points)
d. What is the R squared for the model? (2 points)
e. What is the t statistic for ₁at the 5% level of significance? (2 points)
Λ
f. What is the 95% confidence interval for B₁? (2 points)
Λ
g.…
Problem 2
Hypothesis Testing
Suppose you are interested in the effect of neighborhood crime incidents on high school
graduation rates. You run the following regression model:
Graduation; ßo+ß₁Crime; +ɛ¿
=
You would like to test whether the neighborhood crime incidents have a statistically
significant effect on high school graduation rate at the 5% level of significance (α = 0.05).
You estimate the model and find that B₁ = -0.04 and se (B₁) = 0.008.
a. Write down the null hypothesis and alternative hypothesis. (4 points)
b. Calculate thet statistic of B₁. (5 points)
C. What is the critical value of thet statistic for the 5% level of significance? (2
points)
d. Calculate the 95% confidence interval for the coefficient on Crime? (6 points)
e. Based on your answers to the questions b, c, and d, do you reject or fail to reject the
null hypothesis you defined in question a? Justify your answer. (5 points)
Λ
f. Isẞ₁ statistically significant at the 5% level? (3 points)
Chapter 3 Solutions
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